Threshold functions for asymmetric Ramsey properties involving cycles

We consider the binomial random graph G_p and determine a sharp threshold function for the edge-Ramsey property for all l₁,…,l_r, where C^l denotes the cycle of length l. As deterministic consequences of our results, we prove the existence of sparse graphs having the above Ramsey property as well as the existence of infinitely many critical graphs with respect to the property above. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 245–276, 1997